Speaking about Tuesday's veto, Bush said "Yesterday was a day that highlighted differences.
"Today is a day where we can work together to find common ground."
Democrat leaders who emerged from the meeting called the session positive but said their main goal was to find a way to end the four-year-old Iraq war, in which 3,300 Americans and countless Iraqis have been killed.
Munzir Baig, Muscat, Oman
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Nancy Pelosi, the house speaker, said: "Whatever our differences, we owe it to the American people to find our common ground.
"Of course, we must stand our ground if we can't find it. But we must strive to find that common ground."
No easy compromise was within reach.
Both parties agree the proposed spending bill should include benchmarks for progress in Iraq, but many Democrats insist they be tied to timelines for US troop withdrawals if they are unmet.
Bush and his Republican congressional allies say such links are unacceptable.
Robert Gates, the defence secretary, suggested the problem may not be the benchmarks themselves, but spelling out consequences - such as troop withdrawals - if the Iraqis fail to meet the targets.
"I think one of the issues will be: To what degree are there consequences involved if one or another benchmark isn't met?" he said at the Pentagon.
'Deadline for failure'
Bush said on Tuesday that he recognised the Democrat-controlled congress's statement against the war made through the bill, but said US troops needed funding without further delay.